Energy-momentum method for co-rotational plane beams: A comparative study of shear flexible formulations

This paper presents an energy-momentum method for three dynamic co-rotational formulations of shear flexible 2D beams. The classical midpoint rule is applied for both kinematic and strain quantities. Although the idea as such was developed in previous work, its realization and testing in the context of co-rotational Timoshenko 2D beam elements is done here for the first time. The main interest of the method is that the total energy and momenta are conserved. The three proposed formulations are based on the same co-rotational framework but they differ in the assumptions done to derive the local formulations. Four numerical applications are used to assess the accuracy and efficiency of each formulation. In particularly, the conservation of energy with a very large number of steps and the possibility to simplify the tangent dynamic matrix are investigated.